Hipparchus himself basing on his calculation of the tropical year and 
on the Metonic cycle constructed a period of 304 (4 X 4 X 19) years 
minus one day = 111,035 days which period comprises 3,760 synodical 
months. (See Ideler’s Chronology, I, p. 352.) The advantages of this 
period are that it comprises integral numbers of civil days and of lunar 
months and, very nearly, of tropical years while at the same time it 
implies nearly accurate estimations of the length of the year and the 
month, (viz., 365*^^ 5^^ 55' 15" and 29^^ 12^^ 44' 2‘5"; the accurate figures 
according to Hipparchus being 365^^ 5^ 55' 12" and 29^ 12^ 44' 3‘2"). 
A period of this kind would, however, apparently not have suited Indian 
purposes. We here are met by one of the particular Indian require¬ 
ments which helped to transform systems of Creek origin into the Indian 
systems with their strongly marked peculiarities. At the time when 
Greek astronomy began to act on India the calendar in prevalent use in 
the latter country was undoubtedly already the well-known lunisolar one 
with its tithis and intercalary lunar months. The peculiarity of this 
calendar is, that it does not inform one directly of the number of civil 
days which have expired from the beginning of the current year but 
only of the number of the elapsed lunar days or tithis. From the latter 
the number of civil days has to be derived by means of a proportion. 
And again in order to ascertain the number of tithis contained in a 
certain number of years antecedent to the current year, it is necessary 
at first to ascertain the number of intercalary lunar months which have 
occurred in the course of those years, a process requiring the employ¬ 
ment of another proportion. We cannot enter in this place into a 
discussion of the reasons which may have led to the adoption of such an 
extraordinary and inconvenient style of calendar ; for our purposes it is 
sufficient to know that it had established itself on Indian soil at an early 
period. It appears for instance in the Jyotisha-Vedahga, although the form 
in which it there presents itself is a comparatively simple and primitive one, 
the writer of the Yedahga neither having an accurate knowledge of the 
length of the revolutions of the sun and the moon nor being acquainted 
with the solar and lunar inequalities. At any rate it had taken a firm 
hold on the Hindu nation and when Greek notions and methods streamed 
in, they had to adapt themselves to the existing system. Thus the above 
described manner of calculating the number of civil days comprised in 
a certain period with its twofold transformation of solar years into lunar 
months and of lunar days into civil days required the establishment of 
arithmetical mean taken between the sidereal year of Hipparchus and that of the 
Clialdeans has not much to recommend itself j the mean would not even be an 
accurate one. 
